hdu5047 Sawtooth 规律 + JAVA大数

Sawtooth

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 2272    Accepted Submission(s): 834

Problem Description

Think about a plane:

● One straight line can divide a plane into two regions.
● Two lines can divide a plane into at most four regions.
● Three lines can divide a plane into at most seven regions.
● And so on...

Now we have some figure constructed with two parallel rays in the same direction, joined by two straight segments. It looks like a character “M”. You are given N such “M”s. What is the maximum number of regions that these “M”s can divide a plane ?

 

Input

The first line of the input is T (1 ≤ T ≤ 100000), which stands for the number of test cases you need to solve.

Each case contains one single non-negative integer, indicating number of “M”s. (0 ≤ N ≤ 10 ¹²)

 

Output

For each test case, print a line “Case #t: ”(without quotes, t means the index of the test case) at the beginning. Then an integer that is the maximum number of regions N the “M” figures can divide.

 

Sample Input

  
  

   
   2
1
2
  
  

 

Sample Output

  
  

   
   Case #1: 2
Case #2: 19
  
  

 

f(n) = 8 * n * n - 7 * n + 1

import java.io.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(new BufferedInputStream(System.in));
		PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		int T, kase;
		T = in.nextInt();
		kase = 0;
		BigInteger n, ans;
		while (T-- != 0) {
			n = in.nextBigInteger();
			ans = BigInteger.valueOf(8).multiply(n).multiply(n).subtract(BigInteger.valueOf(7).multiply(n))
			.add(BigInteger.ONE);
			out.printf("Case #%d: ", ++kase);
			out.println(ans.toString());
		}
		
		in.close();
		out.close();
	}
}